Abstract

A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann ﬂuid. The membrane is represented by a set of massless points which advect with the ﬂuid and which impose forces on the ﬂuid which are derived from a free energy functional with a value which is dependent upon the geometric properties of the membrane. The method is validated in two dimensions with a free energy functional which imposes the constraint of constant membrane length, constant enclosed area, a bending rigidity and a preferred curvature. The method is shown to recover the expected equilibrium shape in the absence of ﬂow and deformation in the presence of an applied shear ﬂow. The method may have applications in a number of mesoscopic simulations, including discrete models of blood cells.